Problem 273//Beat the clock
Larry Laggard is frequently, if not always, late for everything. This morning, after sleeping through his alarm, Larry awakes to the sound of his telephone ringing. When he picks it up, the voice on the other end says, “This is Mr. B. Ontime of Tick Tock Watches. Congratulations! You have won one of our $5,000 gold watches. All you have to do to claim your prize is be at our store after 4 p.m., but before the time when the minute hand completely hides the hour hand. One second late, and you lose.”
Larry is thrilled. He has never won a prize before, and people are always telling him he needs a watch. Larry plans on sitting down to figure out exactly when he needs to be at the store to claim his prize, but by the time he showers, gets dressed, eats lunch, and returns his overdue library books, he has to leave. On the way, he gets stuck in a traffic jam caused by construction.
He finally gets to Tick Tock Watches at 4:15 p.m. What time does Larry need to walk through the door to win his watch? Give your answer to the nearest second.
This month’s problem was submitted by Ron Arreola of Chicago.